The Representation And The Uniqueness Of The Solution Of The Volterra Integral Equation Of The Second Kind And The Related Problems Pure Mathmatics

This paper mainly discusses the representation and the uniqueness of the solution of the Volterra integral equation of the second kind and the related problems.This paper consists of two chapters.In chapter one, This paper summarizes the history and the source of the integral equations, and explains the transformation of differential equation to integral equation, and gives some related definitions and concepts. The successive approximation method and the existence and the uniqueness theorem of the solution of the Fredholm integral equation of the second kind in [17] are also shown. The singular integral equation with Cauchy kernel is showed in the last part of this chapter.In chapter two, similar to [3], the successive approximation method of the solution of the Volterra integral equation of the second kind is studied. The definition of the kernel of the Volterra integral equations of the second kind is obtained. The existence and the uniqueness theorem of the solution of the Volterra integral equation of the second kind with nonweakly and weakly singular kernel is introduced. Some of the main properties are derived. At last, systems of the Volterra integral equations are simply introduced.